A383283 Indices of record low-water marks of the sequence abs((cos n)^n).

0, 1, 2, 5, 8, 11, 33, 55, 77, 99, 121, 143, 165, 187, 190, 209, 212, 234, 256, 278, 300, 322, 344, 366, 633, 655, 677, 699, 721, 1032, 1054, 1076, 1387, 1409, 1431, 1764, 2119, 2474, 2829, 3184, 3539, 3894, 4249, 4604, 4959, 5314, 5669, 6024, 6379, 6734, 7089, 7444, 7799, 8154, 8509, 8864, 9219, 9574, 9929, 10284

Offset

0,3

Links

Table of n, a(n) for n=0..59.

Example

The first few values of abs((cos n)^n) are:
  abs(cos(0)^0) = 1
  abs(cos(1)^1) = 0.540302305868139
  abs(cos(2)^2) = 0.173178189568194
  abs(cos(3)^3) = 0.970276937921503
  abs(cos(4)^4) = 0.182542548055270
  abs(cos(5)^5) = 0.001836568887601
  abs(cos(6)^6) = 0.783591241730686
  abs(cos(7)^7) = 0.138422055397017
  abs(cos(8)^8) = 0.000000200865224
  abs(cos(9)^9) = 0.432737211396127
and the record low points are at n = 0, 1, 2, 5, 8, ...

Mathematica

Module[{x, y, runningMin = 1.1, positions = {}},
  x = Range[0, 10^6]; y = Abs[Cos[x]^x];
  Do[If[y[[i]] < runningMin, runningMin = y[[i]]; AppendTo[positions, i-1]; ], {i, Length[y]}];
  positions
]

Prog

(Python)
from mpmath import iv
running_min, A383283 = 2, []
for i in range(1033):
    while True:
        x = abs(iv.cos(i)**i)
        if (comparison:=x<running_min) is None:
            iv.dps += 1
            running_min = abs(iv.cos(A383283[-1])**A383283[-1])
        else: break
    if comparison:
        A383283.append(i)
        running_min = x
print(A383283)  # Jwalin Bhatt, Jan 05 2026

Crossrefs

Cf. A382564, A383229.

Sequence in context: A246442 A056661 A229883 * A135050 A004112 A024815

Adjacent sequences: A383280 A383281 A383282 * A383284 A383285 A383286

Keyword

nonn

Author

Jwalin Bhatt, Apr 28 2025

Status

approved